Hydrologic Analysis PART 1 Hydrology and Floodplain Analysis Chapter 2 CEVE /512 Dr. Phil Bedient Jan 2018

Unit Hydrograph Theory Hydrology and Floodplain Analysis, Chapter 2.2 Unit Hydrograph Theory

Unit Hydrograph Defined as 1-in of precipitation spread uniformly over a watershed in a given duration 0.5 hr UH 1 hr UH 3 hr UH Used to easily represent the effect of rainfall on a particular basin Hypothetical unit response of watershed to a unit of rainfall

UH Example 2-Hr UH Note that 0.5 in/hr fall for the 2 hours

UH Applications Development of design storm hydrograph Development of watershed hydrograph

UH developed from a single storm Total storm hydrograph Hydrograph minus baseflow, rainfall minus losses Hydrograph adjusted to be a 2-hr UH

Concerns with UH s Assumptions of linearity are inherent in UH development Linearity can be violated if… intensity variations are large over long-duration storms Storage effects in watershed are important Typically should not exceed areas of 3 – 5 mi2 in urban areas, 10 sq mi natural A Divide the watershed into subareas if needed

S-Curve Method Allows for the construction of UH of any duration Creating the S-Curve Add and lag series of UH of duration, D, by time period D Gives runoff hydrograph from continuous rainfall excess intensity of 1/D Equilibrium hydrograph or an S-Curve

S-Curve Method S-Curve to UH Shift the curve by D’ hr Subtract ordinates between the two curves Receive curve (b) Multiply all ordinate by D/D’ Receive UH of duration D’

Unit Hydrograph Convolution Deriving hydrographs from multiperiod rainfall excess or Where Qn = storm hydrograph ordinate Pi = rainfall excess Uj = UH ordinate where j = n - i + 1

Unit Hydrograph Convolution Can view this graphically Note that the final hydrograph goes to time-step 10 UH goes from 0-7 4 Rainfall periods of 1 time step

UH Convolution Example Pn= [0.5, 1.0, 1.5, 0.0, 0.5] in Un= [0, 100, 320, 450, 370, 250, 160, 90, 40, 0] cfs

UH Convolution Example Pn= [0.5, 1.0, 1.5, 0.0, 0.5 ] in UH Time (hr) P1Un P2Un P3Un P4Un P5Un Qn 1 50 2 160 100 260 3 225 320 150 695 4 185 450 480 1115 5 125 370 675 1220 6 80 250 555 1045 7 45 375 805 8 20 90 240 535 9 40 135 300 10 60 140 11 12 13

Unit Hydrograph Convolution Can reverse procedure Multiperiod rainfall excess hydrograph  UH Uses matrix methods [Q] = [P][U]  [PTP][U] = [PT][Q]  [U] = [PTP]-1[PT][Q]

Synthetic Hydrograph Development Hydrology and Floodplain Analysis, Chapter 2.3 Synthetic Hydrograph Development

Synthetic Unit Hydrographs – 60s UHs developed for ungaged basins Based on data for similarly gauged basins Revolutionized ability to predict hydro response Produce storm hydrographs from rainfall data Can be updated to reflect changes in watershed geography/land cover Variety of approaches but most based on tp (lag time) and Qp (peak flow)

Synthetic Methods Snyder’s Method (1938) - ** Clark Method (1945) – TC & R** Nash IUH (1958) SCS (1957, 1964) – Soil Conserv Serv. Kinematic Wave (1970s) - **

Snyder’s Method (1938) First to develop a synthetic UH Studied watersheds in Appalachian Highlands Simple and popular method tp = Ct*(L*Lc)0.3 Tp = lag time (hr) Ct = coeff. (1.8-2.2) L = length of main stream (mi) Lc = length to centroid (mi) Qp = 640*Cp A/tp Qp = peak flow (cfs) Cp = coefficient (0.4-0.8) A = area (sq mi) Tb = 3 + tp/8 Tb = time base of hydrograph (days)

Snyder’s Method (1938) Example Skecth the approximate shape of hydrograph for an area of 100 mi2 Given: Ct = 1.8 L = 18 mi Cp = 0.6 Lc = 10 mi tp = Ct*(L*Lc)0.3 = 8.6 hr Qp = 640*Cp A/tp = 4465 cfs Tb ~ 4tp = 34.4 hr Duration = tp/5.5 hr = 1.6 hr

SCS Method - Triangle Early method assumed a simple triangle hydrograph with certain parameters D – rain duration (hr) TR – time of rise (hr) B – time of fall (hr) QP – peak flow (cfs) tP – lag time from centroid of rainfall to QP

SCS Method - Triangle Volume of direct runoff from hydrograph Where

SCS Method - Triangle Lag Time Lag time (tP) is most often estimated using formula below – 3000 watersheds Make sure units match L = length to divide (ft) y = average watershed slope (%) S = 1000/CN – 10” CN = curve number from soil/land use table

Clark UH Method (1945) Based on the use of a watershed Handout from CHAP 5 Modeled as a linear channel in series with a linear reservoir Accounts for translation and attenuation Creates instantaneous UH (IUH) from the outflow (Oi) from the linear reservoir Inflow (Ii) to the linear reservoir is the outflow from the linear channel